Plasmonic enhancement of spatial dispersion effects in prism coupler experiments

Recent experiments with film-coupled nanoparticles suggest that the impact of spatial dispersion is enhanced in plasmonic structures where high wave-vector guided modes are excited. More advanced descriptions of the optical response of metals than Drude's are thus probably necessary in plasmonics. We show that even in classical prism coupler experiments, the plasmonic enhancement of spatial dispersion can be leveraged to make such experiments two orders of magnitude more sensitive. The realistic multilayered structures involved rely on layers that are thick enough to rule our any other phenomenon as the spill-out. Optical evanescent excitation of plasmonic wave guides using prism couplers thus constitutes an ideal platform to study spatial dispersion.

Figure 1

Schematic representation of the prism couplers: (a) resembles the Otto configuration, i.e., a prism on top of a metallic slab, which ensures coupling to the gap plasmon, while (b) resembles the Kretschmann-Raether configuration, i.e., a prism on top of a dielectric layer through which the guided modes of an IMI structure are coupled.

Figure 2

(a) Reflectivity in the local approximation (solid black line) and with the hydrodynamic model (dashed red line) for the MIM structure with air. The dashed black line corresponds to the coupler without the second metallic interface. The vertical dotted line shows where the undisturbed surface plasmon is expected. For large gaps, only the surface plasmon on the lower interface is excited. For the thinner gap, the symmetric and antisymmetric modes can clearly be seen. The angle of excitation for the symmetric mode is higher than for the SP, signaling the gap-plasmon regime. (b) Same situation with a dielectric loaded gap and a lower frequency. The impact of nonlocality begins to be noticeable because the resonance is at larger incidence angle.

Figure 3

Reflectivity of the structure shown in Fig. 1 as a function of the incident angle ${\theta }_i$ for two values of $h_{\text{gap}}$. The wavelength of the incident light is $\lambda =600$ nm. The prism is made of ${\text{TiO}}_2$ with a permittivity ${\epsilon }_p=6.78$, the metal is Au with a permittivity ${\epsilon }_m=-8.44+1.41i$, and the dielectric is air. The upper metallic layer thickness is $h_c=18$ nm. The resonance corresponds to the excitation of a gap plasmon.

Figure 4

Reflectivity of the structure shown in Fig. 1 as a function of the incident angle ${\theta }_i$ for two values of $h_{\text{gap}}$. The wavelength of the incident light is $\lambda =750$ nm. The prism is made of ${\text{TiO}}_2$ with a permittivity ${\epsilon }_p=6.41$, the metal is Au with a permittivity ${\epsilon }_m=-18.50+1.50i$, and the dielectric is LASF9 with a permittivity ${\epsilon }_d=3.37+1.10e^{-07}i$. The thickness of the upper metallic layer is $h_c=18$ nm.

Figure 5

Reflectivity of the structure shown in Fig. 1 as a function of the incident angle ${\theta }_i$ for $h_m=44$ nm. The wavelength of the incident light is $\lambda =700$. Prism is ${\text{TiO}}_2$ with permittivity ${\epsilon }_p=6.50$, metal is Au with permittivity ${\epsilon }_m=-15.04+1.31i$, and dielectric is LASF9 with permittivity ${\epsilon }_d=3.28+1.15\times {10}^{-07}i$ (a permittivity very close to one of the other high index dielectrics like ${\text{Al}}_2{\text{O}}_3$). The thickness of the layer under the prism is $h_c=65$ nm. The two dips are due to the excitation of LRSP (left) in the plain regime and SRSP (right) in the near coupling regime.